Given two points a & b, find the equation of a line that connects a & b that minimizes the surface area of the shape created by revolving the line about the x axis. use variational methods.

For the closed feedwater heater below, feedwater enters state 3 at a pressure of 2000 psia and temperature of 420 °f at a rate of ix10 ibhr. the feedwat extracted steam enters state 1 at a pressure of 1000 psia and enthalpy of 1500 btu/lbm. the extracted er leaves at an enthalpy of 528.7 btu/lbm steam leaves as a saturated liquid. (16) a) determine the mass flow rate of the extraction steam used to heat the feedwater (10) b) determine the terminal temperature difference of the closed feedwater heater

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis

With increases in magnification, which of the following occur? a. the field of view decreases. b. the ambient illumination decreases. c. the larger parts can be measured. d. the eyepiece must be raised.